3-D unitary ESPRIT for joint 2-D angle and carrier estimation

It is essential for an efficient frequency and time slot allocation procedure in future mobile communication systems using space division multiple access (SDMA) to determine the mobiles that are spatially well separated from one another. Thus, once a mobile desires to initiate a call, precise knowledge of the 2-D arrival angles of its dominant wavefronts is required. In this application, 3-D Unitary ESPRIT for joint 2-D angle and carrier estimation offers an efficient way to handle such mobile access requests since it provides efficient high-resolution measurements of the spatial characteristics of the wireless channel, even if only a small number of antennas is available at the base station. Automatic pairing of the 3-D estimates is achieved via a new simultaneous Schur decomposition (SSD) of three real-valued, non-symmetric matrices. In general, the SSD enables an R-dimensional extension of Unitary ESPRIT (R≥3) to estimate several undamped R-dimensional modes or frequencies along with their correct pairing in multidimensional harmonic retrieval problems. Here, we present a Jacobi-type method to calculate the SSD. For each of the R dimensions, the corresponding frequency estimates are obtained from the real eigenvalues of a real-valued matrix. The SSD jointly estimates the eigenvalues of all R-matrices and, thereby, achieves automatic pairing of the estimated R-dimensional modes via a closed-form procedure that neither requires any search nor any other heuristic pairing strategy.